Mater dicit nos aestate frui debere, praesertim cum Iulius aut Augustus calidissimus sit.

It has two layers:

• Mater dicit = Mother says
• nos aestate frui debere = that we ought to enjoy the summer

Latin often uses an indirect statement after verbs like dicit. Instead of English that we ought..., Latin uses:

• an accusative subject: nos
• an infinitive verb: debere

Then frui depends on debere, and aestate goes with frui.

So the structure is:

• Mater = subject
• dicit = main verb
• nos = subject of the indirect statement
• debere = infinitive in the indirect statement
• frui = complementary infinitive with debere
• aestate = object of frui in the ablative

Because it is inside an indirect statement after dicit.

English says:

• Mother says that we ought to enjoy summer.

Latin normally says:

• Mother says us to ought to enjoy summer
  which is not natural English, but shows the Latin pattern: accusative + infinitive

So:

• direct statement: Nos aestate frui debemus = We ought to enjoy summer
• indirect statement after dicit: Mater dicit nos aestate frui debere

That is why debere is infinitive.

Nos is the subject of the indirect statement.

That may feel strange to an English speaker, because in English the subject stays nominative: we. But in Latin indirect statement, the subject becomes accusative.

So:

• nos ... debere = that we ought ...

A small complication is that nos looks the same in both nominative and accusative. So you have to recognize its function from the construction, not just from the form.

Because fruor, frui is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

So:

• frui does not mean to be enjoyed
• it means to enjoy

This is a very common thing in Latin, and fruor is one of the standard examples.

Because frui takes the ablative, not the accusative.

So:

• aestate frui = to enjoy summer / summertime

This is something you simply have to learn with the verb:

• fruor
  • ablative

For an English speaker, that feels unusual, because English enjoy takes a direct object. Latin does not always match English patterns.

Not primarily. Here it is best understood as the ablative object of frui.

That is important because aestate could, in another sentence, mean in summer as an ablative of time when. But in this sentence, because of frui, it is tied to the verb enjoy:

• aestate frui = to enjoy summer / the summertime

So the verb is controlling the case.

It is debere plus an infinitive.

• debeo = I ought / I must / I owe
• frui = to enjoy

So:

• frui debere = to ought to enjoy
• in normal English: to ought to enjoy is awkward, so we say to have to enjoy or more naturally to ought to enjoy only in explanation
• in full context: that we ought to enjoy summer

In other words, debere expresses obligation or advisability, and frui tells you what that obligation is about.

Because this cum clause uses the subjunctive.

Latin very often uses:

• cum + subjunctive

for a clause giving background, circumstance, or reason. Here the idea is something like:

• especially when July or August is very hot
• or especially since July or August is very hot/the hottest

So sit is subjunctive because the clause is not just a plain factual time-marker; it gives surrounding circumstance or explanation.

Yes. That is one reason cum clauses can feel slippery to English speakers.

With the subjunctive, cum often has a sense like:

• when
• since
• although

depending on context.

Here praesertim and the overall sense make especially when or especially since both plausible. The exact English wording depends on how the translator wants to bring out the nuance.

Because aut means or: one alternative or the other.

The sense is:

• July or August
• that is, either July or August

So Latin can treat that as singular in sense, and therefore use:

• sit not sint
• calidissimus not calidissimi

If the sentence had et = and, then a plural would be expected.

It can mean either, depending on context.

The Latin superlative often works in two ways:

• true superlative: hottest
• intensive sense: very hot

So calidissimus sit could be understood as:

• is the hottest
• or is very hot

In a sentence about July and August, many readers will naturally hear the hottest, but very hot is also a possible shade of meaning.

Because Latin can use the month names by themselves.

So:

• Iulius = July
• Augustus = August

Latin does not need to add mensis every time. Just as English says July and August, Latin can simply use the names alone.

Praesertim means especially.

It emphasizes the point that follows:

• Mother says we ought to enjoy summer, especially when/since July or August is very hot

So it highlights the cum clause as an especially important reason or circumstance.